Such an exhaust volume is known from the patent application filed under no. FR 11 59216. This application describes an exhaust manifold in which waves can be arranged easily. The manifold described in that application comprises an exhaust duct and a flange, the flange including a cannon made up of a first segment extended by a second segment that is not as thick as the first segment, and is connected to the wall of the exhaust duct. The second segment of the flange and the wall of the exhaust duct are typically secured to one another by brazing. The wall of the exhaust duct covers the second segment over the entire height of said second segment. Due to the large size of the overlap, brazing allows a particularly strong connection of the first and second cannons to one another. However, patent application no. FR 11 59216 does not describe how to connect the duct to the cannon when the cannon is enclosed in a double cooling jacket, or more generally an outer neck.